Problem:
Consider two firms A and B that are identical in all respects except capital structure. Firm A has $100 million in equity outstanding and $40 million in bonds outstanding. Firm B has $140 million in equity outstanding and $0 million in bonds outstanding. There are no taxes.
(A). Suppose an investor has a $5 million investment in the stock of firm A. What alternative $5 million investment that includes firm B's stock will give the investor the same cash flow payoff in future years as his current investment in firm A's stock? (Hint: I am looking for the amount of cash you would invest in firm B's stock and the amount of cash you would either invest in other securities or borrow from other sources so that $5 million comes out of your pocket today and you get the exact same cash payoff down the road as the current $5 million investment in firm A's stock. See the Modigliani and Miller proof.)
(B) Suppose an investor has a $7 million investment in the stock of firm B. What alternative $7 million investment that includes firm A's stock will give the investor the same cash flow payoff in future years as his current investment in firm B's stock? (Hint: I am looking for the amount of cash you would invest in firm A's stock and the amount of cash you would either invest in other securities or borrow from other sources so that $7 million comes out of your pocket today and you get the exact same cash payoff down the road as the current $7 million investment in firm B's stock. See the Modigliani and Miller proof.)
Please provide all workings and formulas.